When Tinariwen leader Ibrahim Ag Alhabib comes out after a few songs sung by bandmate Abdallah Ag Alhousseyni, he shatters any notions of an international cool barrier. Maybe it's that he is the only band member not in robes, his head not wrapped in a taguelmoust; instead his hair erupts into a bushy Hendrix/Santana halo as he and the band drone out on beautiful African blues. Or perhaps it's the beatific bliss somehow radiating from his unsmiling, solemn persona. But there is no mistaking the coolnessthe something he knows that we, the audience, do notwhich is especially manifest as he fits his voice into the six-strong mix; the band immediately finds the full-bodied warmth of their sublime new album, Tasili, recorded in the southeastern Algerian desert.

One wonders how often Tinariwen had to compete with the thudding bass '80s-themed dance parties in the "empty spaces" of Mali. (Their name is derived from the Tamashek word for that phrase.) That decade surely brings back a whole different set of memories for the desert blues band, performing as a septet on Saturday night at Webster Hall, where an '80s-themed rager went on in the downstairs area.

Though it is perhaps the first of the band's recordings to play more like an album and less like documentation, Tassili (Anti-) has fifth-album syndrome throughout. It's topped with guests (from Wilco, TV on the Radio, and the Dirty Dozen Brass Band) and has a back-to-the-roots mission about playing songs around campfires that would read like parody if not for the band's origins. If there is no all-star American talent at Webster Hall, probably thankfully, there is also very little of the new album's sublime and quiet folk, which is sort of a bummer. The band is instead in workingman's Tinariwen mode, a hard-touring band on the worldwide circuit.

At least making a case for itself against the booming bass below, the band's sole percussionSaid Ag Ayad's handdrumis mixed loudly, almost snapping atop the dreamy guitars like gunfire. At times, Ayad gets up and moves toward the front of the stage to receive cheers, one of a few bits of showbiz pizzazz displayed onstage during the evening. Bassist Eyadou Ag Leche steps out often (maybe too often) with thumb-popping bass fills that give the music, at times, an unwelcome jambandy turn.

However far their home actually is from the Village on a weekend night, it probably seems much further; there is little of Tassili's perfect grace in the hour-and-a-half performance. But despite all conspiring against it, the music is instantly familiar and transporting. Though Tinariwen never listened to American blues, one can make a parlor game out of spotting the melodic connections to songs like "Gospel Plow" (especially in their gang call-and-response numbers) and the Baptist hymn "Oh My Loving, Brother," more famously adapted by Woody Guthrie for "This Land Is Your Land." From the throats of Ibrahim Ag Alhabib and company, though, the melodies carry with whatever meaning they had before words were attached. The guitars are prominent and properly luminous, though the solos are short, and the three players rarely stretch above the 12th frets, a trickto the western ear, anywayof a subtle modesty that gives the music an unflashy hypnotic quality. Many of the songs end suddenly, too, as if all their secret knots had been untied and it is simply time to finish.

For the encore, Ibrahim Ag Alhabib comes out by himself with an electric guitar and begins a song solo. His playing is almost Jandek-like, a kind of magical droning nonchalance that has more empty space than the whole night combined, his face a nearly perfect blank. It's not the desert that Tinariwen are trying to find from the stage in New York, but a third place they are trying to get to from wherever they are at the moment; while he is playing alone Ibrahim Ag Alhabib seems to arrive there fully. The rest of the band return midway through, get the crowd clapping, and join in. It is dramatic, and probably the right move for the encore. Later, Ibrahim Ag Alhabib even cracks a bit of a smile, but the door has been closed.

Critical bias: Tassili will probably make my year-end list; I listened to it over and over this year. But I had to Google 75% of the background info above.